The compensation arrangement announced in January involves no salary or cash bonus but sets up rewards for Musk based in part on electric vehicle maker Tesla's market value rising to $650 billion over the next 10 years, from around $56 billion currently.

Palo Alto, California based Tesla is under pressure as its much-anticipated Model 3 sedan has already missed several key production targets.

ISS calculated the award was worth $3.7 billion on the grant date, compared with the $2.6 billion projected by Tesla. It joins advisory firm Glass Lewis in recommending against the proposal.

Tesla shareholders are due to vote on March 21, and the company needs majority approval for the proposal to go through. The company declined to comment.

The award "locks in unprecedented high pay opportunities for the next decade, and seemingly limits the board's ability to meaningfully adjust future pay levels in the event of unforeseen events or changes in either performance or strategic focus," ISS said on Thursday.

The advisory firm also flagged that a big part of the award could be earned even if Tesla, which reported its worst ever loss in the fourth quarter, does not sustainably make profits in the future.

"Musk's financial interests are already strongly aligned with Tesla; it is questionable whether an additional $2.6 billion grant is necessary or appropriate to further align his interests when he already owns a 22 percent stake in the company," ISS added.

Some analysts have questioned whether billionaire Musk's other interests, from space exploration to tunnel boring technology, are a distraction at what is seen as a critical time for Tesla.

Musk took to Twitter on Thursday to call on U.S. President Donald Trump to challenge Chinese auto trade rules.

Tesla shares were down half a percent at $327.25 after markets closed on Thursday.